In a vehicle equipped with a multistep automatic transmission (including a non-stage transmission which performs stepped transmission (CVT: Continuously Variable Transmission), etc. Henceforth, it may be referred to as an “AT.”), the number of gear shift stages tends to increase, for example, for the purpose of further improving fuel consumption and/or acceleration performance, etc.
On the other hand, in a cruise control device (including an adaptive cruise control (ACC) device, etc. Henceforth, it may be collectively referred to as a “CC.”), it has been known to carry out acceleration control accompanied by what is called “gradient restriction” in which an upper limit is set for an increment of the acceleration per unit time (increase rate of acceleration) (alternatively, driving force or torque), for example, at the time of an initiation of constant-speed running control (will be mentioned later in detail) and a reversion (resume) after release of the constant-speed running control, etc., for example, for the purpose of reducing worsening of an operation feeling associated with rapid alteration of acceleration, etc. (for example, refer to the Patent Document 1 (PTL1)).